Question

A and B can do a piece of work in 72 days, B and C can do it in 120 days, A and C can do it in 90 days.At what can A alone do it? ​

Answer 1

Let A,B and C take a,b and c days to complete the work alone.

so in one day A will do (1/a)th work

while in one day B will do (1/b)th work

and in one day C will do (1/c)th work.

A and B can together do a work in 72 days.

so in one day A and B will do (1/72)th work.

1/a + 1/b = 1/72 ---------(1)

1/b = 1/72 - 1/a --------(2)

B and C can together do a work in 120 days

so in one day B and C will do (1/120)th work

1/b + 1/c = 1/120 --------(3)

1/b = 1/120 - 1/c ---------(4)

A and C can together do a work in 90 days

so in one day A and C will do (1/90)th work.

1/a + 1/c = 1/90 --------(5)

1/72 -1/a = 1/120 - 1/c -------- from (2) & (4)

1/c -1/a = 1/180 ---------(6) (after solving we get this)

Let 1/c = x and 1/a = y

x+y=1/90 ------ from(5)

180x + 180y = 2 -----(7) (multiple by 180 we get this)

x - y = 1/180 (from 6)

180x - 180y = 1 ----------(8)

after solving (7) and (8) we get ,

y = 1/360

resubstitute y = 1/360 in 1/a

so a = 360

hence A can alone take 360 days to complete the work

mark brainliest